%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN247-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:35 AM UTC 2025
% Result : Unsatisfiable 0.24s 0.50s
% Output : Proof 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 29 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 186 ( 91 ~; 79 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 83 ( 75 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(1,plain,
^ [D: $i,E: $i,C: $i] :
refl(( ( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
<=> ( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
<=> ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
<=> ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [D: $i,E: $i,C: $i] :
trans(monotonicity(rewrite(( ( m1(C,C,C)
| ~ q0(D,E) )
<=> ( m1(C,C,C)
| ~ q0(D,E) ) )),
( ( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) )
<=> ( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) ) )),
rewrite(( ( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) )
<=> ( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) )),
( ( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) )
<=> ( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) )
<=> ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,E)
| ~ q0(D,C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_018) ).
tff(7,plain,
! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( q0(e,d)
<=> q0(e,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
q0(e,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_2) ).
tff(13,plain,
q0(e,d),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| ~ q0(e,d)
| m1(d,d,d) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| ~ q0(e,d)
| m1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ( m1(d,d,d)
| ~ q0(e,d)
| ~ q0(e,d) )
<=> ( ~ q0(e,d)
| m1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| m1(d,d,d)
| ~ q0(e,d)
| ~ q0(e,d) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| ~ q0(e,d)
| m1(d,d,d) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| m1(d,d,d)
| ~ q0(e,d)
| ~ q0(e,d) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| ~ q0(e,d)
| m1(d,d,d) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| m1(d,d,d)
| ~ q0(e,d)
| ~ q0(e,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [D: $i,E: $i,C: $i] :
( m1(C,C,C)
| ~ q0(D,C)
| ~ q0(D,E) )
| ~ q0(e,d)
| m1(d,d,d) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
m1(d,d,d),
inference(unit_resolution,[status(thm)],[19,13,10]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(( ~ m1(d,X,Y)
<=> ~ m1(d,X,Y) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : ~ m1(d,X,Y)
<=> ! [Y: $i,X: $i] : ~ m1(d,X,Y) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Y: $i,X: $i] : ~ m1(d,X,Y)
<=> ! [Y: $i,X: $i] : ~ m1(d,X,Y) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Y: $i,X: $i] : ~ m1(d,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(25,plain,
! [Y: $i,X: $i] : ~ m1(d,X,Y),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : ~ m1(d,X,Y),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : ~ m1(d,X,Y),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : ~ m1(d,X,Y)
| ~ m1(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,27,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15 % Problem : SYN247-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 12:29:53 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.24/0.50 % SZS status Unsatisfiable
% 0.24/0.50 % SZS output start Proof
% See solution above
% 0.24/0.52 % E exiting
%------------------------------------------------------------------------------